I think that for right now a flip phone (or any non-smartphone) might reduce your exposure to a smartphone-specific contract tracing system.
But...I have my reservations as to whether the world's governments are limiting their contact tracing efforts to smartphones and digital systems. If I were the FBI and/or a local police dept, I'd be asking the cellular network providers for triangulation data on which IMEIs (this is the serial number attached to the SIM card in your phone, including traditional "dumb" phones) were in the close vicinity of an IMEI belonging to an infected person. There are problems with this approach related to geolocation accuracy, but in my experience accuracy doesn't always stop govt agencies from pursuing gathering up as much information as they can possibly get their hands on. There is also history of the govt pursuing data collection programs from corporate entities in a secret fashion - either forced via National Security Letter or cooperative via NDA - which could mean that this is occurring already and we are not aware of it.
If you carry around a device with a wifi radio in it (e.g., iPod Touch, iPad, laptop) then you need to assume that every wifi access point it comes into contact with is making your efforts at privacy nullified. If you keep such a device powered off then that helps from a location tracking perspective. Then you'll only be tracked when you power the device on and it connects to wifi. Same goes for your computer in this context.
Here's my view on what to do given the following scenarios:
- You absolutely cannot risk any 3rd party knowing your location without your prior consent - buy a faraday bag for each of your digital devices, turn those devices off to prevent unnecessary battery drain, store them in the faraday bags while traveling and while not in use. This will be a major pain in the ass but a faraday bag should block all ingress and egress radio frequencies. For the cellular devices that you do use, buy prepaid SIM cards from stores that do not require your ID when buying them and pay in cash. When you park at the store, park somewhere not in view of any nearby cameras that could read your license plate. You may need to park a few blocks away where there are no cameras and walk to the store from there. Wear clothing that conceals your body shape, wear a face mask, wear glasses that you don't usually wear and wear a hat that you don't usually wear. When you are powering down your internet connected devices, turn their wifi radios off first so that when you power them back up they don't automatically start communicating with nearby access points. Use cash for everything and do not enter your phone number into the machine at the grocery store or use your rewards card at the gas station. Be very aware of digital systems you interact with and always assume they are trying to know who you are. Consider using a privacy-friendly VPN like Mullvad with the Kill Switch option enabled so that your internet does not work when the VPN isn't connected. Pay for the VPN service using Bitcoin or Bitcoin Cash (doing so is its own pain in the ass). This is all the tip of the iceberg but it'll get you started in a pretty secure way. See my notes below on how to stay private otherwise while using the internet.
- You prefer to minimize your privacy risks while also maintaining easy contact with the outside world - buy a "dumb" phone and do not travel with any other devices that are powered on. When you do use an internet connected device use a privacy focused web browser, use NextDNS to block as much as you possibly can, only use Signal for messaging purposes (which means the person you're messaging needs to use Signal too) and do not use any services that leverage Google, Facebook, Twitter or LinkedIn for their back-end systems or analytics. This includes services directly from those companies too of course - Gmail, Google Photos, Facebook, Instagram, WhatsApp, SMS text messages, etc.
- You need access to the internet all the time, including while traveling - consider following my advice above about staying private on the internet. Be aware of the fact that your location is being recorded continuously as you move about and will be made available to various 3rd parties without your consent or knowledge.
I personally require connection constantly due to the nature of the businesses I'm involved with, so I fall into the last scenario which puts me at a high risk of being tracked. This will be the case for most people.
If you fall into one of the first two scenarios, then I'd recommend wading into the requisite territory as an experiment so that you can be sure it's going to work for you before you throw your Android phone or iPhone in the trash. Make sure you can operate your life in a sustainable way for at least a couple weeks before destroying your existing setup.